On Tennis: Amanda Anisimova Leads Young Americans With a Deliberate Pace

“That’s because, in her mind, Amanda’s already been out there before,” said Martin Blackman, the general manager for player development at the United States Tennis Association. “She’s always seen herself competing on the big stages. She’s been preparing for this since she was 8 years old.”

Her potential is clear as she prepares to face another top 10 player, fifth-seeded Karolina Pliskova, in the fourth round on Tuesday.

A letdown is hardly out of the question, but the trick is for no one to get ahead of oneself.

Not the U.S.T.A. Not the news media. Not Anisimova and her already sizable entourage, which includes her father and head coach, Konstantin Anisimov; her mother, Olga; her traveling coach, Max Fomine; her longtime coaching consultant, Nick Saviano; and her longtime agent, Gary Swain; as well as Max Eisenbud, the hard-driving IMG vice president who represents, among others, Maria Sharapova and Madison Keys.

“We’ve got a very long view,” Konstantin Anisimov said. “We are very happy she is doing way better than we expected, to be honest with you, but at the same time we are staying very calm and understanding that she is young. She is still growing, and she is definitely not ready to play a full schedule and at age 16. She is not allowed to play a full schedule. So we are trying to do more quality than quantity.”

Handling precocious success is a longstanding tennis conundrum, even if prodigies no longer dominate the women’s game in their teens like they used to. Playing restrictions, designed to protect them, have kept prospects in their midteens from racking up too many ranking points. The game is now more physical, favoring more mature players, and also has become more team-oriented, favoring those who can afford a large support staff.

Anisimova, the youngest player in the top 150 of the global rankings, is at no disadvantage in that last department, and the entourage also includes her Chihuahua Miley, who gets the star treatment but has also created the occasional travel problem.

“Once we went to Hawaii, and my mom flew for six hours to California and she didn’t know about the quarantine rules for Hawaii,” Anisimova said. “So she had to fly back home another six hours with Miley.”

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Anisimova after defeating her fellow American Cori Gauff for the United States Open junior title last year.Credit Chang W. Lee/The New York Times

Though Anisimova has been a champion-in-training for much of her young life and has been home-schooled from the beginning, her parents, both immigrants from Russia, have shown restraint.

The latest example: Anisimova could have entered qualifying for the Australian Open this year, but she and her family chose to remain in the United States, working on her fitness and refining her game in an extended off-season.

“I didn’t want to make such a long trip, especially because I didn’t get into the main draw of the Australian Open,” Anisimova said. “So I decided to skip that one and have a real off-season. I think I had eight weeks.”

Now 14, Gauff is the youngest of a particularly promising new wave of American women’s players, including CiCi Bellis, already ranked 45th at age 18, and Caroline Dolehide, a fast-improving 19-year-old with a powerful and versatile game who took the first set off the No. 1-ranked Simona Halep on Sunday before losing 1-6, 7-6 (3), 6-2 in the third round.

“It’s really exciting, this new generation that is coming up,” Anisimova said.

The key is to remain focused on improvement even after the contracts and attention begin to roll in.

“I’ve been trying to use my head more when I play,” Anisimova said. “Playing smarter and not just bashing the ball, going for crazy shots all the time. So I am starting to think more and analyze the game. Like, when I’m out of the court and used to go for down-the-line shots — I don’t do that anymore.”

What has also been impressive is the way her power game has held up against power in Indian Wells. She will see plenty more big shots against Pliskova, the flat-hitting and huge-serving former No. 1 from the Czech Republic.

“Amanda’s a very, very good striker of the ball, probably one of the best out there already,” said Higueras, who coached Michael Chang and Jim Courier and is now a master coach consultant with the U.S.T.A. and has frequently visited Anisimova’s practice sessions here.

Higueras continued: “She is very solid from the ground with tremendous power from both wings and a very, very good serve with good volleys. She’s a pretty complete player for being as young as she is. If the people around her are patient enough and process-oriented enough, I think in two, three, four years she will be able to do pretty much everything — some things better than others, but with no holes in her game.”

That is quite a statement from a veteran coach who is not prone to overstating his case. But then anyone who watched Anisimova treat her center-court match against Kvitova like business as usual can see that there is genuine cause for excitement.

“Nobody should get carried away, but she’s a special player,” Blackman said. “With a special ability for handling the moment.”